Ventilatory efficiency (η⩒E) of the exercise: A detailed method report

Ventilatory efficiency is a combination of the ventilatory-metabolic response stemming from non-invasive analysis of cardiopulmonary exercise testing. Despite being a recognized marker in exercise physiology, this measure presents considerable limitations, including the imprecise designation of “efficiency”, broadly recognized, and recently denominated as “excess ventilation”. Herein we present a detailed method, with substantial improvements, and new physiological insights, in order to better define the true ventilatory efficiency of the exercise, according to recommendations for physical/physiological processes.• “Ventilatory efficiency” of the exercise is a remarkable physiological index.• Several limitations are currently debated.• We report a new ventilatory efficiency index that match with recommendations.


Rational
The relationship between minute ventilation ( ∨E ) and carbon dioxide output ( ∨CO 2 ) is a non-invasive physiological mutual response to exercise that is influenced by several factors (e.g., chemosensitivity, ergoreceptors, lung perfusion, etc.), and finely coupled to exercise demands [1] .The ∨E-∨CO 2 slope is a classic marker of "ventilatory efficiency " [2] , and there is large agreement of its importance in clinical settings [2][3][4] .However, there are several points that remain inconclusive with respect to the reliability of the ∨E-∨CO 2 slope.Thus, among the limitations of the ∨E-∨CO 2 slope are (i) the recognized effects of ventilatory mechanical constraints in down-shifting the ∨E-∨CO 2 slope [5 , 6] , (ii) the imprecise use of the designation "ventilatory efficiency " with respect to the ∨E-∨CO 2 slope [ 7 , 8 ], (iii) the imprecise application of linear regression for a quadratic function, that fits better when using the whole exercise time-frame, including the post respiratory compensation point (RCP) data [1] , (iv) the use of a smaller sample of data points for the linear segment of the ∨E-∨CO 2 response, excluding data on remarkable physiological ventilatory responses after the RCP [9] , and (v) the effects of primary hyperventilation [7] .In addition, (vi) severe acidosis could up-shift the ∨E-∨CO 2 slope at the level comparable with cardiopulmonary disease (slope > 35) in athletes [10] , and (vii) recently, several limitations of the ∨E-∨CO 2 slope for endpoint prognostication in cardiopulmonary diseases were described [ 11 , 12 ].The method presented herein is an alternative to the ∨E-∨CO 2 slope, and the first effort at a detailed description of ventilatory efficiency of the exercise (  ∨E ), that is consistent with the true designation of "efficiency " in biology/physiology [13] , characterized by the following criteria: (i) "efficiency is a measure of performance that characterizes an actual performance relative to a perfect level ", (ii) and "must be preferentially presented as a fraction (percentage) of a single process ".This paper substantially improves the method previously published by the same author for validation [ 6 , 14 ].

Exercise protocol and data analysis
The CPET was performed in a Vmax encore 229® device (Viasys Healthcare, Yorba Linda, USA, 2012), controlled by an electric braked cycle ergometer ViaSprint (Viasys Healthcare, Yorba Linda, USA, 2012), under digital oxygen saturation and electrocardiography monitoring (Cardiosoft®, EUA, 2012).Subjects with HF exercised through an incremental protocol to a maximal symptom-limited performance with a 10-20 Watt * min − 1 .Healthy subjects exercised with 25 Watt * min − 1 .Details of the method were published previously [ 15 , 16 ].The individual tests of the exercise phase were analyzed breath-by-breath, with exclusion of values exceeding the standard deviation of the local average by 3-times, before presenting five-breath moving averages for ∨CO 2 -log ∨E slope and  ∨E analysis and the method description.

Method description ∨CO 2 -log ∨E slope
The method is based on measuring the amount of CO 2 cleared by the lungs ( ∨CO 2 , L * min − 1 ) plotted against a predefined range of increase in minute-ventilation ( ∨E ) (ten-fold increase, based on semi-log scale) during incremental exercise to symptom-limited maximum tolerance.During this semi-log construction, in most cases the ∨CO 2 -log ∨E slope stemmed from a quadratic function, with part of the equation better fitted by a true linear function (red line in Fig. 1 A, bottom left).In some individuals, data might present a linear tendency, from the beginning, up to end of the exercise ( Fig. 1 B).Thus, the CO 2 output is represented as a dependent variable (y-axis), and ∨E as the independent variable (x-axis).To achieve a constant rate of CO 2 output, we took the log 10 of the ∨E , as previously described for the oxygen uptake efficiency slope (OUES).During this semi-log plotting, the ∨CO 2 -log ∨E signal is described by a quadratic function, as follow: with the final component of the equation described by a linear function: We termed this slope coefficient ( "b ") as the CO 2 output constant rate ( ∨CO 2 -log ∨E slope), after excluding the non-linear segment.Similar to the OUES, this slope describes the rate of CO 2 output during graded exercise, for each ten-fold increase in ∨E .Subsequently, we ascribed the transition point from the exponential-to-linear part of the ∨CO 2 -log ∨E slope to the beginning of the first ventilatory threshold ( Ɵ L ), after careful analysis of the entire sample.Thus, as we can see in Fig. 2 , the beginning of the linear segment of the ∨CO 2 -log ∨E response is approximately time-aligned with the Ɵ L, both in a representative healthy subject, and in a representative HF participant.This is suggested by the time-alignment with the beginning of both (i) the increase in the ∨E / ∨O 2 , and (ii) the beginning of the isocapnic ventilation "buffering " period for the ∨E / ∨CO 2 equivalent.Thus, the ∨CO 2 -log ∨E slope could be calculated after the exclusion of the data before the Ɵ L .

∨CO 2 -log ∨E max
Furthermore, we assume a formalism for a theoretical maximal constant rate for clearing the CO 2 from the lungs during exercise hyperpnea , or ∨CO 2 -log ∨E max .This theoretical ceiling could be achieved during incremental exercise if we assume a complete  We can see the close relationship between the beginning of the linear part of the V ´CO 2 -log V ´E slope (red line) with the Ɵ L , preceded by the smooth exponential increase (green curve).The transition is coincident with the increase in the ∨E / ∨O 2' (blue circles) combined with the beginning of the ∨E / ∨CO 2 ventilatory isocapnic "buffering " period (green circles).The first vertical interrupted line-arrow points to the Ɵ L transition, and the second vertical interrupted line-arrow points to the probable RCP correspondent projection.At the ∨E / ∨CO 2 ventilatory isocapnic "buffering " period, there is a proportional increase in both ∨E and ∨CO 2 , provoking a relatively flat ∨E / ∨CO 2 profile (between Ɵ L and RCP).Abbreviations: RCP, Respiratory Compensation Point; Ɵ L , First VentilatoryThreshold. uptake of oxygen from the lungs, resulting in an expired fraction of oxygen ( F E O 2 ) of "0 % " and expired carbon dioxide fraction ( F E CO 2 ) of 22 % (for balanced nitrogen).While not physiologically achievable, this situation provides us with the theoretical upper limit for CO 2 output.The maximum CO 2 output attainable, or ∨CO 2 -log ∨E max, can be practically calculated using the predicted MVV, as follows: ∨CO 2 -log ∨E max = MVV predicted * 0.22 * 0.826, where 0.826 is the ATPS to STPD conversion factor assuming ambient temperature and pressure corrections (see Fig. 3 for details).This hypothetical state is in accordance with the definition of "perfection " in physiology (Gans, C., 1991), or "represents the best state that is conceivable.It would thus be equivalent to an efficiency of 100 %.It is obviously the abstract Platonic ideal….. " [13] .

Ventilatory efficiency ( 𝜂 ∨E )
Subsequently, the ∨CO 2 -log ∨E max is compared to the ∨CO 2 -log ∨E slope, defining the true ventilatory efficiency index (  ∨E ,%).Hence, we can measure the actual CO 2 output constant rate during incremental exercise ( ∨CO 2 -log ∨E slope) and represent this as a proportion of the ∨CO 2 -log ∨E max, in order to obtain the  ∨E .This calculation would take the form:  ∨ = ( ∨CO 2 − log ∨E slope ∕ ∨CO 2 − log ∨E max ) * 100 ( Figure 3) The potential advantages of the  ∨E compared to the ∨CO 2 -log ∨E slope are (i) fulfillment of the criteria for a true ventilatory efficiency index, as the actual rate of CO 2 cleared from the lungs is compared to a theoretical ceiling for the same rate of CO 2 (in "% ", as usually required for an efficiency index), and (ii) allowing the adjustment of the ∨CO 2 -log ∨E slope for age, sex, and/or body mass index, depending on reference equations for MVV.When reference equations for MVV are not available, a possible solution is to refer to the predicted FEV 1 multiplied by a factor of 40.However, ideally, reference equations for  ∨E would be the best approach.

Fig. 1 .
Fig. 1.Integrated four-axis representation for ventilatory efficiency.We can see in the right upper axis the quadratic function response for the ∨E -∨CO 2 slope from the start-to-end of exercise.The "red line " comprises the pre-RCP regression function (A).In the left lower is depicted the quadratic function for the ∨CO 2 -log ∨E slope from the start-to-end of exercise response.The "red line " comprises the linear part of the total response (A and B).The left x-axis is represented as log ∨E.Abbreviation: RCP, Respiratory Compensation Point.

Fig. 2 .
Fig.2.Representation of the ∨E / ∨CO 2 and ∨E / ∨O 2' equivalents against log ∨E common x-axis in the Upper Panel, and ∨CO 2 (L) against log ∨E common x-axis in the Lower Panel, respectively for a healthy subject (left) and an HF subject (right).We can see the close relationship between the beginning of the linear part of the V ´CO 2 -log V ´E slope (red line) with the Ɵ L , preceded by the smooth exponential increase (green curve).The transition is coincident with the increase in the ∨E / ∨O 2' (blue circles) combined with the beginning of the ∨E / ∨CO 2 ventilatory isocapnic "buffering " period (green circles).The first vertical interrupted line-arrow points to the Ɵ L transition, and the second vertical interrupted line-arrow points to the probable RCP correspondent projection.At the ∨E / ∨CO 2 ventilatory isocapnic "buffering " period, there is a proportional increase in both ∨E and ∨CO 2 , provoking a relatively flat ∨E / ∨CO 2 profile (between Ɵ L and RCP).Abbreviations: RCP, Respiratory Compensation Point; Ɵ L , First VentilatoryThreshold.

Fig. 3 .
Fig. 3. Example of ventilatory efficiency (  ∨E ) calculation.In this three-axis plot, minute-ventilation was plotted without log scale and placed at the right for clarity.The linear regression of the linear part of the quadratic function is depicted as a red line, and the linear coefficient or actual CO 2 output constant rate ( ∨CO 2 -log ∨E slope) is equal to 3 L * logL ˉ1 for this particular subject (below).The predicted MVV for this subject is 140 L/min and the maximum "assumed " CO 2 output constant rate ( ∨CO 2 -log ∨E max) theoretically predicted for this subject would be 26 L * logL ˉ1 (see the text for elaboration).Thus,  ∨E = ( ∨CO 2 -log ∨E slope / ∨CO 2 -log ∨E max) * 100 = 11,5 %.Reproduced with permission.